Grimshaw received his PhD in musicology, as well as a certificate in world music, from the Eastman School of Music in 2005. He received his bachelor's degree in percussion performance from the University of Utah in 1998. His scholarly articles have appeared in the Musical Quarterly, American Music, The Journal of Musicological Research, and other publications, and he has presented papers on both Western and Eastern musical topics at conferences of The International Musicological Society, the American Musicological Society, the Society for American Music, and other organizations.

Shortly after his arrival at BYU in the fall of 2007, Grimshaw commissioned the construction of a new Balinese gamelan (percussion orchestra) from the shop of I Wayan Berata, Bali's most prestigious composer and instrument maker. During the subsequent school year he became the founding director of Gamelan Bintang Wahyu, BYU's Balinese percussion orchestra. Grimshaw also began to teach a new class for the honors program, which focused on the music of Indonesia.

In 2010, Grimshaw completed a general-audience book on Balinese music titled The Island of Bali is Littered with Prayers ” (Mormon Artists Group, 2010). His other book was published the following year, and is titled “Draw a Straight Line and Follow It: The Music and Mysticism of La Monte Young” (Oxford University Press, 2011).

In 2011, Grimshaw and other faculty and staff at BYU combined to complete the Simon Shaheen Residency Project. The project was funded by the Laycock Center for Creative Collaboration in the Arts, and was a collaborative effort to bring Simon Shaheen and five other Middle Eastern musicians (who now live in the US) to BYU for a four-day residency. Jeff Martin directed the project in conjunction with the Beauty and Belief exhibit in the Museum of Art at BYU.